The study is concerned with the approximation capabilities of fuzzy neural networks with numerical inputs and fuzzy connections in relation to continuous fuzzy-valued functions \(F\). More specifically, \(F:\mathbb{R}\to F(\mathbb{R})\) where \(F(\mathbb{R})\) denotes a family of fuzzy numbers in \(\mathbb{R}\) (namely, fuzzy sets whose \(\alpha\)-cuts are closed intervals in \(\mathbb{R}\), with bounded support and normal membership functions). One studies a neural network governed by the expression \[ Y= \sum^n_{i=1} W_i\Biggl(\sum^m_{j=1} V_{ij} \sigma(xU_j+ \Theta_j)\Biggr) \] whose connections (\(W_i,V_{ij}, U_j\) and \(\Theta_j\)) are regarded as fuzzy numbers with \(\sigma\) being a continuous monotonic function from \(\mathbb{R}\) to \(\mathbb{R}\), and ``\(n\)'' and ``\(m\)'' denoting the number of the nodes in the respective layers. It is shown that this network is a universal approximator of \(F\).